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Mathematics
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Danny Pak-Keung Chan
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Apparently, this user prefers to keep an air of mystery about them.

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  • Member for 2 years, 7 months
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  • Last seen 13 mins ago

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Top posts (177) All Questions Answers | Votes Newest

10 If $\int_a^bg(x)dx=0$, show that $\int_a^bf(x)g(x)dx=0.$ 2 days ago
6 $f_n \rightharpoonup f$, $g_n \to g$ in measure, $\|g_n\|_{L^\infty} \leq M$, then $f_n g_n \rightharpoonup fg$, Jun 30 '18
5 Proof: If $f : [a,b] \to [0,M]$ is Riemann integrable and has integral zero then $f(x) = 0$ at every continuity point $x$ of $f$. Jul 22 '17
4 Is this true: $\mathbb{E}(f(X)g(Y)) = \mathbb{E}(f(X))\mathbb{E}(g(Y))$ if $X,Y$ are independent? Aug 7 '17
4 Question about arbitrary set intersections. Oct 24 '17
4 ${a_n}\rightarrow L$ and {$f_n$}$\rightarrow f$ pointwise. Does it follow that $f_n(a_n)\rightarrow f(L)$ Apr 21 '18
4 Does $\int_{-\infty}^\infty f(x) dx < \infty$ where $f \ge 0$ implies $\sup_{x \in \mathbb R} f(x)<M $? Nov 21 '18
4 $X_i$, $i=1,2,..n$ independent R.Vs $P(X_i=1)=\frac{3}{4} ,\ P(X_i=-1)=\frac{1}{4}$. Prove $\sum_{i=0}^nX_i \to \infty$ a. s. as $n \to \infty$ May 19
3 For $f \in L^2 (\mathbb{R}), g(x) = \int_x^{x+1}f(t)\mathrm{d}t$ show $\lim_{x \to\infty} g(x) = 0$ May 10
3 Prove $\int \bigg(\sum_{n=1}^{\infty} f_n \bigg) d \mu = \sum_{n=1}^{\infty} \bigg( \int f_n d \mu \bigg) $ Mar 8
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